What do you think of Thucydides' treatment of early Greek history? What sources does he use? Could he have done a better job treating this period?

I'd suggest it would be a mistake to judge Thucydides by modern historical standards (be aware, in the context of the study of history, he's positioned as one of its earliest practitioners, and when it comes to his analytic rigor, he represents a substantial leap forward compared to his predecessor Herodotus). We should make allowances for his status as a classical historian and one of those individuals who shaped history into the field of study we know today.
So, when you look at his use of sources, be aware that he did not have the access to modern methodologies or extensive documentation generated by modern societies; with that in mind, he tended to rely heavily on eyewitness accounts, as well as on his own personal experience (he did serve as an Athenian general during the Peloponessian War). He remains far less credulous in his treatment of fact and supposition than Herodotus appears to have been before him, and he is far more stringent in his approach to historical truth.
That being said, Thucydides is also quite known for his wholesale re-creation of speeches. When he presents Pericles's Funeral Oration, for example, this is not an actual transcription of Pericles's words but rather a dramatic invention on Thucydides's part, intended to recreate the essence of Pericles's meaning. For modern historians, such reinvention would be viewed as dubious, but again, you should make allowances for time and era and recognize the ways in which classical history will not match up to modern standards.
Where I would say Thucydides really excels, however, is in his analysis of politics and ideology. One might well suggest that Thucydides, long before Machiavelli, invented the concept of realpolitik, as he was the first to really assert that political decision-making is ultimately founded solely upon self interest, rather than on moral and ethical concerns. In his histories, Athens comes across as purely amoral in its political decision-making, acting solely for its own pragmatic self interest. To pull toward a more specific example, I've always been of the impression that his analysis of civil strife and factionalism (found in book III) looks remarkably modern in its insights, and one can easily imagine this same general vision being re-applied to the kind of chaos unleashed during the French or the Russian Revolutions:

So revolutions broke out in city after city, and in places wherever the revolutions occurred late the knowledge of what had happened previously in other places caused still new extravagances of revolutionary zeal . . . To fit in with the change of events, words too had to change their usual meanings. What used to be described as a thoughtless act of aggression was now regarded as the courage one would expect to find in a party member; to think of the future and wait was merely another way of saying one was a coward. . . . Fanatical enthusiasm was the mark of a real man, and to plot against an enemy behind his back was perfectly legitimate self defence. Anyone who held violent opinions could always be trusted and anyone who objected them became a suspect. To plot successfully was a sign of intelligence, but it was still cleverer to see a plot was hatching (Thucydides, History of the Peloponnesian War [Penguin Classics ed.], transl. Rex Warner, New York: Penguin, 1972, p. 242)

The description goes on, but there's a remarkable sense of timelessness in this vision that reaches beyond the classical world toward a scope that is more universal in its insight into human experience. I would suggest that this is where Thucydides as a historian particularly shines.